The Inverse Distance method

The inverse distance algorithm is used extensively for quick contouring. It works by defining a grid of cells and then estimating a value for each cell based on the surrounding data points. The inverse of the square of the distance from the centre of a grid cell to each point contributing to the estimate of the cell is used to weight the data values. The sum of the weights adds up to one. This means that data close to the point being estimated is given a much higher weighting than data further away. Note that this is an Isotropy algorithm.

The shape of the contours derived using inverse distance, is influenced by the cell density and the search radius. If the cell density is too low (large cells), the contours become very square. A high cell density will give smoother contours. The overall pattern of contours produced by the inverse distance algorithm can suffer from ‘bulls eyes’ and the projection of high contour values into areas that contain no data points.

When the search radius is too small, it is possible to get grid cells that do not have any values as there are no data points in the search area. Increasing the search radius ensures that all grid cells have values and smooths the resulting grid as more points are used in each estimate.

If the search radius is too large, the contour grid will contain cells that have been estimated using only one or two values at the edge of the search area, projecting data into areas with no data.

The bulls eye effect occurs when very high or very low values occur near to the centre of a cell. These are then given a very high weighting which tends to produce an overly large or small value for that grid cell. The result is a bulls eye pattern of contours.

The projection of data into areas that contain no data points is common to most grid-based contouring algorithms. It occurs when a cell is formed in an area with no data and the search algorithm finds only one point at the extreme edge of the search. This one value is then used to estimate the value of the cell. This problem can be countered by ensuring that the data being contoured extends to the edge of the display. However, this may not always be possible, particularly if the data being contoured is unevenly distributed across the area being contoured. In such a situation there may be both internal and external regions on the contouring grid where there is insufficient data to ensure a proper estimate of the grid from several points.

The inverse distance algorithm generally provides a good set of contours for imprecise data. For example: gold grades or geophysical values. This type of data is imprecise because the ‘surface’ which is interpreted as describing the variations in the value of interest can never be accurately predicted, even with extremely dense sample patterns. The best that can be hoped for is an estimate of the form of the surface that has minimal errors. That is, the difference between the actual value at any point on the grid and the estimated value is minimised. It should also be noted that this algorithm does not honour the data points and will result in a surface that has a smaller data range than the original data.